Abstract
In this paper a novel methodology for estimating the parameters for an extended biokinetic model (Peev, Schönerklee, and De Wever, Water Science and Technology, 2004) of micropollutant removal in wastewater treatment is presented. In particular, the work concentrates on parameter estimation of the micropollutant degradation sub-model by specialised microorganisms in the case when only substrate measurement data are available. We have proven the structural identifiability of the model and have developed a new approach allowing practical identifiability on the basis of multiple substrate degradation curves with different initial concentrations. Experimental and related numerical methods for unambiguous parameter estimation have been developed. Finally, by means of simulated pseudo-experiments we have found convincing indications that the proposed algorithm is stable and yields appropriate parameter estimates even in unfavourable regimes.




Similar content being viewed by others
Explore related subjects
Discover the latest articles and news from researchers in related subjects, suggested using machine learning.Abbreviations
- X :
-
biomass (μg COD l−1)
- S :
-
substrate (μg COD l−1)
- μ :
-
growth rate (d−1)
- μ max :
-
maximum growth rate (day−1)
- K s :
-
saturation constant (μg COD l−1)
- Y :
-
growth yield
- b :
-
biomass decay rate (day−1)
- t :
-
time (day)
- mp:
-
micropollutant
- 0:
-
initial condition at t = 0
References
Criddle, C. S. (1993). The kinetics of co-metabolism. Biotechnology and Bioengineering, 41(11), 1048–1056.
Dochain, D., & Vanrolleghem, P. A. (2001). Dynamical modeling and estimation in wastewater treatment processes. London, UK: IWA Publishing.
Dochain, D., Vanrolleghem, P. A., & Van Daele, M. (1995). Structural identifiability of biokinetic models of activated sludge respiration. Wat. Res, 29(11), 2571–2578.
Gernaey, K., Petersen, B., Dochain, D., & Vanrolleghem, P. A. (2002). Modelling aerobic carbon source degradation processes using titrimetric data and combined respirometric-titrimetric data: Structural and practical identifiability. Biotechnology and Bioengineering, 79, 754–769.
Henze, M., Grady, C. P. L. J., Gujer, W., Marais, G. V. R., & Matsuo, T., (1987). Activated sludge model no. 1. Scientific and Technical Report 2, IWAQ, London.
Henze, M., Gujer, W., Mino, T., Matsuo, T., Wentzel, M. C., & Marais, G. v. R. (1995). Activated sludge model No. 2. IAWQ Scientific and Technical Report, No. 3, IAWQ, London.
Holmberg, A. (1982). On the practical identifiability of microbial growth models incorporating Michaelis–Menten type nonlinearities. Mathematical Biosciences, 62(1), 23–43.
Peev, M., Schönerklee, M., & De Wever, H. (2004). Modelling the degradation of low concentration pollutants in membrane bioreactors. Water Science and Technology, 50(5), 209–218.
Penrose, R. (1956). On best approximate solution of linear matrix equations. Proceedings of the Cambridge Philosophical Society, 52, 17–19.
Petersen, B. (2000). Calibration, identifiability and optimal experimental design of activated sludge models. Ph.D. Thesis in Applied Biological Sciences, BIOMATH, University of Gent. Downloadable from http://biomath.ugent.be/publications/download/.
Petersen, B., Gernaey, K., Henze, M., & Vanrolleghem, P. A. (2003). Calibration of activated sludge models: A critical review of experimental designs. In S. N. Agathos, & W. Reineke (Eds.), Biotechnology for the environment: Wastewater treatment and modeling, waste gas handling (pp. 101–186). Dordrecht, The Netherlands: Kluwer.
Petersen, B., Gernaey, K., & Vanrolleghem, P. A. (2001). Practical identifiability of model parameters by combined respirometric-titrimetric measurements. Water Science and Technology, 43(7), 347–355.
Vanrolleghem, P. A., Daele, M. V., & Dochain, D. (1995). Practical identifiability of a biokinetic model of activated sludge respiration. Water Research, 29(11), 2561–2570.
Vanrolleghem, P. A., Insel G., Petersen B., Sin G., De Pauw D., & Nopens I. (2003). A comprehensive model calibration procedure for activated sludge models. Proceedings 76th Annual WEF Conference and Exposition. Los Angeles, USA, October 11–15 (on CD-ROM).
Acknowledgement
The presented work was carried out within the framework of the project PTHREE (www.pthree.de) financed under contract number EVK1-CT-2002-00116 by the European Commission (FP5).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Schoenerklee, M., Peev, M. Parameter Estimation in Biokinetic Degradation Models in Wastewater Treatment—A Novel Approach Relevant for Micropollutant Removal. Water Air Soil Pollut 196, 89–99 (2009). https://doi.org/10.1007/s11270-008-9759-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11270-008-9759-z